We know that the Sith wanted revenge.
But was the whole idea of infiltrating the Republic and taking it over from the top something that Darth Sidious came up with, or was it a generic plan that the Sith had before him?
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The idea was centuries old, an initiative coming down the Sith line of succession from Darth Bane himself. Palpatine was just the one who finally made it happen.
The Grand Plan, also known as the Sith imperative, was a plot by the Order of the Sith Lords that was centuries in the making. The Plan was a precise formula for eradicating the Jedi Order, tearing down the Galactic Republic, and replacing both with a Sith-ruled galaxy.
The plan was devised and initiated by the founder of the Order of the Sith Lords, Darth Bane, and carried out by all the subsequent Sith of his order's lineage.
The overarching Sith plot, called the Grand Plan, had existed since Darth Bane's time and did involve taking over the Republic:
Like Plagueis, Tenebrous had obviously embraced the fact that Darth Bane’s Rule of Two had expired. Precious few Sith Lords had honored it, in any case, and with good reason, as Plagueis saw it. The goals of the Grand Plan were revenge and the reacquisition of galactic power. But while most Sith Lords since Bane had in their own fashion helped to weaken the Republic, their efforts had owed less to selflessness and allegiance to the Rule than to weakness and incompetence.
[Palpatine] was a manifestation of dark purpose, helping to advance the Sith Grand Plan and gradually gaining power over himself so that he might one day—in the words of his Master—be able to gain control over another, then a group of others, then an order, a world, a species, the Republic itself.
Darth Plagueis, pp. 78, 171
However, some of the particulars (especially the use of the clone army) seems to have been devised by Sidious himself. As he betrayed and murdered his master Darth Plagueis (just as he became Supreme Chancellor), Sidious told Plagueis:
I might not have been able to take the final steps to the chancellorship without your help in manipulating the Senate and bringing into play your various and sundry allies. If it’s any consolation, I’m being honest when I say that I could not have succeeded without you. But now that we’ve won the race, I’ve no need for a co-chancellor. Your presence, much less your unnecessary counsel, would only confuse matters. I have Maul to do what the risk of discovery might not allow me to do, while I execute the rest of the Grand Plan: growing an army, fomenting rebellion and fabricating intergalactic war, corralling the Jedi and catching them unawares...
“Rest easy in your grave, Plagueis. In the end, I will be proclaimed Emperor. The Sith will have had their revenge, and I will rule the galaxy.”
Darth Plagueis, p. 359